The present invention relates to a scanning optical system employed in a scanning optical device such as a laser beam printer or the like.
In a scanning optical system for a laser beam printer, a laser beam emitted by a laser diode is deflected by a polygonal mirror to scan within a predetermined angular range. The scanning beam passes through an fxcex8 lens, which converges the beam to form a scanning beam spot on a photoconductive surface. As the polygonal mirror rotates, the beam spot moves on the photoconductive surface. By ON/OFF modulating the beam spot as it moves, an electrostatic latent image is formed on the photoconductive surface. Hereinafter, a direction, on the photoconductive surface, in which the beam spot moves as the polygonal mirror rotates is referred to as a main scanning direction, while a direction perpendicular to the main scanning direction, on the photoconductive surface, is referred to as an auxiliary scanning direction.
Further, shape and direction of power of each optical element is described with reference to directions on the photoconductive surface. Further, a plane perpendicular to a rotation axis of the polygonal mirror and including an optical axis of a scanning lens is defined as a main scanning plane.
Sometimes, a multi-beam scanning optical system is configured such that a plurality of beams are deflected simultaneously by a single polygonal mirror. With such a configuration, since the single polygonal mirror is used as a deflector for each of the plurality of beams, the number of optical elements can be decreased, and a room for such elements can be reduced. If the plurality of beams are respectively inclined in the auxiliary scanning direction, and are incident on substantially the same point on the polygonal mirror, the thickness of the polygonal mirror can be reduced, which reduces a manufacturing cost of the polygonal mirror.
However, if a laser beam is incident on the polygonal mirror as inclined in the auxiliary scanning direction, a bow occurs, that is, a scanning line, which is defined as a locus of a beam on a surface to be scanned, curves.
In addition, the degree of a curve of the scanning line varies according to an incident angle of the laser beam impinging on the polygonal mirror in the auxiliary scanning direction. Therefore, if the multi-beam scanning optical system is configured to form more than one scanning line at predetermined intervals on one photoconductive surface simultaneously, a distance between adjacent scanning lines varies according to positions in the main scanning direction. Such a change of the distance between adjacent scanning lines is called a differential bow.
Since both of the bow and the differential bow deteriorate an imaging accuracy, these should be suppressed particularly for a high-resolution scanning system.
It is therefore an object of the invention to provide an improved scanning optical system that is configured to compensate for the bow and the differential bow while satisfying essential characteristics for a scanning optical system such as a fxcex8 characteristic, correction of a curvature of field and the like.
For the object, according to the invention, there is provided a scanning optical system for emitting at least one beam scanning in a main scanning direction. The scanning optical system is provided with a light source that emits at least one beam, an anamorphic optical element that converges the at least one beam emitted by the light source in an auxiliary scanning direction, a polygonal mirror that rotates and deflects the at least one beam emerged from the anamorphic optical element to scan in the main scanning direction within a predetermined angular range, and an imaging optical system that converges the at least one beam deflected by the polygonal mirror to form at least one beam spot on a surface to be scanned, the at least one beam spot scanning in the main scanning direction on the surface to be scanned.
In the above configuration, the imaging optical system has a scanning lens, and at least one compensation lens provided on the surface side with respect to said scanning lens, the at least one compensation lens compensating for curvature of field. Further, one surface of the scanning lens has an anamorphic aspherical surface, said anamorphic aspherical surface being defined as a surface whose curvature in the auxiliary scanning direction at a point spaced from an optical axis thereof in the main scanning direction is determined independently from a cross-sectional shape thereof along the main scanning direction.
Further, one surface of the at least one compensation lens has an aspherical surface, the aspherical surface being defined as a surface in which a tilt angle of a cross-sectional shape in the auxiliary scanning direction changes with a position in the main scanning direction, the aspherical surface being asymmetrical with respect to a plane perpendicular to the auxiliary scanning direction and including a central point thereof.
With this configuration, it becomes possible to determine a power of the imaging optical system in the auxiliary scanning direction independently from a power in the main scanning direction. Accordingly, it becomes possible to compensate for a bow and a differential bow which are aberrations in the auxiliary scanning direction.
Since, with the above configuration, a curve of a scanning line (i.e., a bow) is well suppressed, it is not necessary to use a toric surface in the imaging optical system. Therefore, all surfaces except for the anamorphic aspherical surface of the scanning lens and the aspherical surface of the compensation lens can be formed as rotational symmetrical surfaces.
In a particular case, the anamorphic aspherical surface of the scanning lens may be configured such that a cross-sectional shape thereof in the auxiliary scanning direction is formed as an arc.
Optionally, the curvature of the anamorphic aspherical surface in the auxiliary scanning direction may decrease as a distance from the optical axis increases.
In a particular case, the aspherical surface of the at least one compensation lens may be defined by a two-dimensional polynomial expression in which a SAG amount between a point on the aspherical surface and a plane tangential to the aspherical surface at the central point is defined by coordinates along the main scanning direction and the auxiliary scanning direction.
Optionally, the tilt angle of the cross-sectional shape of the aspherical surface in the auxiliary scanning direction may increase as a distance from the central point of said aspherical surface increases. By using the aspherical surface defined by the two-dimensional polynomial expression, it becomes possible to prevent a widening of the beam spot due to a fluctuation of a wavefront.
In another case, the light source may emit a plurality of beams, the plurality of beams including first beams whose incident angles with respect to the polygonal mirror in the auxiliary scanning direction are different from each other. Further, the scanning lens may have a single lens through which the plurality of beams deflected by said polygonal mirror pass, and the at least one compensation lens may, include a plurality of compensation lenses through which the first beams pass, respectively.
Optionally, the plurality of beams may include second beams whose incident angles with respect to the polygonal mirror in the auxiliary scanning direction are substantially the same, and the second beams emerged from the scanning lens enter the same compensation lens.
Further optionally, the anamorphic aspherical surface of the scanning lens may be symmetrical with respect to a line intersecting the optical axis and parallel with the main scanning direction, and the aspherical surface of each of the plurality of compensation lenses may be symmetrical with respect to a line intersecting the central point thereof and parallel with the auxiliary scanning direction.
Further optionally, the first beams may include two beams, incident angles of the two beams with respect to the polygonal mirror in the auxiliary scanning direction having opposite signs and absolute values of the incident angles of the two beams being the same, and two of the plurality of compensation lenses through which the two beams respectively pass are arranged such that the two of the plurality of compensation lenses are symmetrical with respect to a line extending along the optical axis of the scanning lens.
In another case, the first beams may include inner beams and outer beams, incident angles of the outer beams with respect to said polygonal mirror in the auxiliary scanning direction are greater than those of said inner beams. In such a configuration, the scanning optical system may satisfy a condition:
0.95xc3x97xcex94xcex2xe2x89xa6xcex94dx/dzxe2x89xa61.05xc3x97xcex94xcex2
where,
xcex94xcex2=xcex2out/xcex2in; 
xcex94dx/dz=(b2xe2x88x92b1)/(a2xe2x88x92a1); 
xcex2out is an angle when incident angles of the outer beams in the auxiliary scanning direction with respect to said polygonal mirror are represented by xc2x1xcex2out;
xcex2in is an angle when incident angles of said inner beams in the auxiliary scanning direction with respect to said polygonal mirror are represented by xc2x1xcex2in;
a1 is an angle when angles formed between the inner beams situated at a central position within the predetermined angular range and the anamorphic aspherical surface of said scanning lens are represented by xc2x1a1, the angles xc2x1a1 being defined in a plane parallel with an auxiliary scanning plane that is a plane parallel with a rotational axis of said polygonal mirror and including the optical axis of the scanning lens;
a2 is an angle when angles formed between the inner beams situated at a marginal position within the predetermined angular range and the anamorphic aspherical surface of said scanning lens are represented by xc2x1a2, the angles xc2x1a2 being defined in a plane parallel with the auxiliary scanning plane;
b1 is an angle when angles formed between the outer beams situated at a central position within the predetermined angular range and the anamorphic aspherical surface of said scanning lens are represented by xc2x1b1, the angles xc2x1b1 being defined in a plane parallel with the auxiliary scanning plane; and
b2 is an angle when angles formed between the outer beams situated at a marginal position within the predetermined angular range and the anamorphic aspherical surface of said scanning lens are represented by xc2x1b2, the angles xc2x1b2 being defined in a plane parallel with the auxiliary scanning plane.
Alternatively or additionally, the scanning optical system may satisfy a condition:
0.9xc3x97xcex94xcex2xe2x89xa6xcex94dx0/dz0xe2x89xa61.1xc3x97xcex94xcex2
where,
xcex94xcex2=xcex2out/xcex2in; 
xcex94dx0/dz0=(b20xe2x88x92b10)/(a20xe2x88x92a10); 
a10 is an angle when angles formed between the inner beams situated at a central position within the predetermined angular range and aspherical surfaces of corresponding compensation lenses for the inner beams are represented by xc2x1a10, the angles xc2x1a10 being defined in a plane parallel with an auxiliary scanning plane that is a plane parallel with a rotational axis of said polygonal mirror and including the optical axis of the scanning lens;
a20 is an angle when angles formed between the inner beams situated at a marginal position within the predetermined angular range and the aspherical surfaces of corresponding compensation lenses for the inner beams are represented by xc2x1a20, the angles xc2x1a20 being defined in a plane parallel with the auxiliary scanning plane;
b10 is an angle when angles formed between the outer beams situated at a central position within the, predetermined angular range and aspherical surfaces of corresponding compensation lenses for the outer beams are represented by xc2x1b10, the angles xc2x1b10 being defined in a plane parallel with the auxiliary scanning plane; and
b20 is an angle when angles formed between the outer beams situated at a marginal position within the predetermined angular range and the aspherical surfaces of corresponding compensation lenses for the outer beams are represented by xc2x1b20, the angles xc2x1b20 being defined in a plane parallel with the auxiliary scanning plane.
In another case, the scanning lens may have a first lens made of plastic and a second lens made of glass.
Alternatively, the scanning lens may have a single lens made of plastic.
Alternatively, the compensation lens provided for each of the first beams may have a single lens made of plastic.
In another case, the light source may emit a plurality of beams including first beams and second beams, the first beams impinging on one reflection surface of the polygonal mirror and the second beams impinging on another reflection surface of the polygonal mirror. In this case, the first beams include two beams, incident angles of the two beams of the first beams with respect to the one reflection surface of the polygonal mirror in the auxiliary scanning direction having opposite signs, absolute values of the incident angles of the two beams of the first beams being the same. Further, the second beams include two beams, incident angles of the two beams of the second beams with respect to the other reflection surface of the polygonal mirror in the auxiliary scanning direction having opposite signs, absolute values of the incident angles of the two beams of the second beams being the same. Further, the scanning lens includes first lens and second lens, the first beams deflected by the one surface of the polygonal mirror passing through the first lens, the second beams deflected by the other surface of the polygonal mirror passing through the second lens. Further, the at least one compensation lens includes four single lenses, each of the four single lenses compensating for curvature of field, four beams including the two beams of the first beams and the two beams of the second beams passing through the four single lenses, respectively.
In another case, the anamorphic aspherical surface of the scanning lens may be configured such that the cross-sectional shape in the main scanning direction is defined as a function of a distance, in the main scanning direction, from the optical axis of the scanning lens, and the curvature in the auxiliary scanning direction is defined as a function of a distance, in the main scanning direction, from the optical axis, the cross-sectional shape in the main scanning direction and the curvature in the auxiliary scanning direction being defined independently from each other.